如何使用基本代数运算来计算加速度计的旋转矩阵

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英文:

How to calculate rotation matrix for an accelerometer using only basic algebraic operations

问题

This C function calculates a rotation matrix based on accelerometer sensor input. It doesn't use trigonometric functions but normalizes input values and uses equivalent equations. Limitations include potential division by zero when the denominator is zero. It ensures the z-axis aligns with gravity. The code simplifies calculations for readability.

英文:

There is a C function that gets the acceleration values of x,y,z of an accelerometer sensor (MEMS IMU) as input, and calculates the rotation matrix in a way that the z axis is aligned with the gravity. It is being used for calibrating the accelerometer data.


#define X_AXIS (0u)
#define Y_AXIS (1u)
#define Z_AXIS (2u)

static float matrix[3][3];
void calculate_rotation_matrix(float raw_x, float raw_y, float raw_z)
{ 
  const float r = sqrtf(raw_x * raw_x + raw_y * raw_y + raw_z * raw_z);
  const float x = raw_x / r;
  const float y = raw_y / r;
  const float z = raw_z / r;

  const float x2 = x * x;
  const float y2 = y * y;

  matrix[X_AXIS][X_AXIS] = (y2 - (x2 * z)) / (x2 + y2);
  matrix[X_AXIS][Y_AXIS] = ((-x * y) - (x * y * z)) / (x2 + y2);
  matrix[X_AXIS][Z_AXIS] = x;
  matrix[Y_AXIS][X_AXIS] = ((-x * y) - (x * y * z)) / (x2 + y2);
  matrix[Y_AXIS][Y_AXIS] = (x2 - (y2 * z)) / (x2 + y2);
  matrix[Y_AXIS][Z_AXIS] = y;
  matrix[Z_AXIS][X_AXIS] = -x;
  matrix[Z_AXIS][Y_AXIS] = -y;
  matrix[Z_AXIS][Z_AXIS] = -z;
}



float result[3];
void apply_rotation(float x, float y, float z)
{
  result[AXIS_X] = matrix[X_AXIS][X_AXIS] * x
                 + matrix[X_AXIS][Y_AXIS] * y
                 + matrix[X_AXIS][Z_AXIS] * z;
  
  result[AXIS_Y] = matrix[Y_AXIS][X_AXIS] * x
                 + matrix[Y_AXIS][Y_AXIS] * y
                 + matrix[Y_AXIS][Z_AXIS] * z;
  
  result[AXIS_Z] = matrix[Z_AXIS][X_AXIS] * x
                 + matrix[Z_AXIS][Y_AXIS] * y
                 + matrix[Z_AXIS][Z_AXIS] * z;

}

I'm trying to wrap my head around how it works and why there is no use of trigonometric functions here?
is it just simplifying the trigonometric functions by normalizing the input values and using the equivalent equations to calculate the trigonometric functions?

What are the limitations of this method? for example when the denominator calculated is zero, we will have division by zero. Anything else?

Tried to search on the internet and stackoverflow, but couldn't find a similar method to calculate the rotation matrix.

UPDATE:

Just simplified the calculations so they are more readable.
To add more context this code is used to rotate the readings of an accelerometer in a way that regardless of the orientation of the device, the z-axis is perpendicular to the ground.

The calculate_rotation_matrix() is called when we know that the object is stationary and is on a flat surface. This results in calculating the 3x3 matrix. Then the apply_rotation() is used to rotate subsequent readings.

答案1

得分: 0

四元数表示可以在不使用三角函数的情况下应用旋转。但这似乎是https://math.stackexchange.com/a/476311的一个版本。数学似乎是其中的一个变种,其中"a"和"b"分别是加速度计和重力向量。

该方法还似乎假设测量不会完全准确。而MEMS传感器符合这一描述。否则,正如您所述,如果x和y都为零,那么就会出现除以零的情况。

英文:

A quaternion representation can apply rotations without trig functions. But this appears to be a version of: https://math.stackexchange.com/a/476311 . The math appears to be a variation thereof, where "a" and "b" are the accelerometer and gravity vectors.

The method also appears to assume measurements will not be perfect. And MEMS sensors fit that description. Otherwise, as you stated, if x and y are both zero then you have a divide by zero condition.

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  • 本文由 发表于 2023年6月1日 11:26:14
  • 转载请务必保留本文链接:https://go.coder-hub.com/76378492.html
  • accelerometer
  • calibration
  • imu
  • mems
  • rotational-matrices
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